Random forests are theoretically funded on the assumption that the data are i.i.d. realizations from a multivariate random vector $(X_1, \ldots, X_p, Y)$. Does it make sense to use random forests (for prediction and for feature selection based on variable importance) when the predictive variables are not i.i.d. from a multivariate vector $(X_1, \ldots, X_p)$ ? For instance when there is a "trend" in some covariates or when covariates are controlled during the experiments (a fixed design) ? Obviously it makes no sense to consider a variable importance as an estimate of the population variable importance in such a situation. But can we consider that nevertheless, the variable importances are relevant ?


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